A336313 - OEIS

A336313

Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A336125(i)) = A278222(A336125(j)) for all i, j >= 1.

1, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 4, 3, 2, 2, 2, 3, 3, 2, 2, 5, 2, 2, 3, 3, 2, 2, 2, 3, 4, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 3, 3, 2, 2, 5, 2, 2, 4, 5, 2, 2, 2, 3, 3, 3, 2, 5, 2, 2, 3, 3, 3, 2, 2, 3, 6, 2, 2, 5, 2, 2, 3, 3, 2, 2, 3, 3, 3, 2, 2, 5, 2, 2, 4, 3, 2, 2, 2, 3, 3

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OFFSET

1,2

COMMENTS

Restricted growth sequence transform of A278222(A336125(n)).

For all i, j: A336311(i) = A336311(j) => a(i) = a(j) => A336123(i) = A336123(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

PROG

(PARI)

\\ Needs also code from A336124:

up_to = 1024; \\ 65537;

rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };

A253553(n) = if(n<=2, 1, my(f=factor(n), k=#f~); if(f[k, 2]>1, f[k, 2]--, f[k, 1] = precprime(f[k, 1]-1)); factorback(f));

A336125(n) = if(n<=2, n-1, (1==A336124(n))+(2*A336125(A253553(n))));

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523

A278222(n) = A046523(A005940(1+n));

v336313 = rgs_transform(vector(up_to, n, A278222(A336125(n))));

A336313(n) = v336313[n];

CROSSREFS

Cf. A253553, A278222, A336124, A336125.

Cf. also A292585, A336311, A336312, A336123.

Sequence in context: A165074 A374152 A273165 * A095139 A109038 A208246

Adjacent sequences: A336310 A336311 A336312 * A336314 A336315 A336316

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jul 17 2020

STATUS

approved